Upper Bounds on Superconducting and Excitonic Phase Stiffness for Interacting Isolated Narrow Bands

This work develops a systematic theoretical framework to determine the low-energy effective ``diamagnetic'' response associated with superconductivity and excitonic superfluidity in strongly interacting electronic models hosting isolated nearly flat bands. The results can be used to derive upper bounds on the transition temperatures for superconductivity and excitonic superfluidity without making any mean-field type approximations. The same theoretical framework can also be extended with very few modifications, to address questions related to ferromagnetism in flat bands and magnetic circular dichroism.